Is there a way to control the precise pixel-level position and size of custom fields on a Custom Page or standard screen, rather than manually lining fields up one at a time using the little arrow buttons?

Answer

Yes, via editing exported profile XML directly: place the custom field on the screen and nudge it slightly using the arrow buttons first, which seeds coordinate values into your personal profile; re-log in so your personal profile saves those seeded coordinates; then open your own personal profile, locate the specific screen's Layout branch, which will show the custom field's entry with Top/TopLabel-style position values among its other layout entries, and export that Layout branch as XML using its RMB option. Edit the specific numeric position/size values directly in the exported XML file, then re-import that same branch back in using a replace-import option, and restart the application to see the precise new layout take effect. This is considerably faster than repeatedly nudging fields one arrow-click at a time to get many custom fields precisely aligned and evenly spaced.